Integrating CD4 data into undiagnosed estimates

Use CD4 at diagnosis to increase the precision of undiagnosed HIV estimates from the testing history model

Why

• The testing history model relies heavily on the inter-test interval, and the distribution of infection probability across that interval.

  • For cases diagnosed on their first test, or with negative tests that are far in the past, this creates a long window of possible infection.
  • Assuming the distribution of infection probability is uniform across that interval decreases the precision of our estimate
  • These cases are not very informative regarding time of infection in our current model

• High CD4 measured at diagnosis is an indicator of recent infection

  • So it can be used to identify cases with long windows who are likely to have been infected recently.

How

• Identify typical times from infection associated with CD4 counts from the research literature;

• Use this to reallocate the probability of infection within long infection windows.

• NOTE: we only reallocate from a uniform distribution towards more recent infection when indicated by higher CD4. We do not reallocate towards a less recent infection when indicated by low CD4. So the potential impact on the undiagnosed estimate is only possible in one direction: to reduce the undiagnosed fraction.

Impact in WA

• Modest reduction in estimates of undiagnosed cases (about 10%)

• Consistent with the findings from the previous analysis incorporating the BED for recent infection, but with more confidence because the level of missing data is much lower for CD4 (25% vs. 70% for the BED)

• But we need to be careful now because our key remaining assumptions may be leading to downward bias in our estimates.

Introduction

1. Review of the Testing History method for estimating undiagnosed cases of HIV

2. Review of key testing history data descriptives in WA State

3. How we integrate CD4 data into the method

Results

1. CD4 data descriptives in WA State

2. Impact on estimated median time since infection, and time spent undiagnosed

3. Impact on estimated undiagnosed cases in 2014

Distributes probability of infection uniformly across the possible infection window

Longer windows have less probability assigned to the recent period

The hazard (instantaneous rate) of infection at any point within the window is 1/(window length), shown by the red line for each window lengths. Time = 0 refers to time of diagnosis.

The cumulative probability of diagnosis is the area under the curve. The 2-year window assigns greater probability of infection within the last year than the 5-year window, shown by the grey shaded region.

The age distribution of never-testers will influence the window lengths they contribute to the analysis.

Effect of age on windows for never-testers

Testing histories = Tested + Never Tested

Breakdown of testing histories in WA HIV cases 2005-2014.

Total N = 5148
With testing history N = 3016.

66% of MSM versus 43% of non-MSM have testing histories

Testing history by group (Percents are within group)

• MSM comprise about 2/3 of cases.
  

• What is driving differential response rates?

Distribution of infection window lengths in years (N = 3016)

Labels indicate bounds, e.g. (0,1] includes windows >0 and <= 1. The 18-year windows are never-testers (NT).

• These cases will not be modified by CD4 counts

Distribution of infection window lengths in years (N = 3016)

• These are the cases with the greatest potential for CD4 modification, but only if their CD4 counts at diagnosis are high.

• Less than half of these cases are never-testers (13/31 = 42%).

Distribution of infection window lengths by group (Percents are within group)

• 58% of non-MSM have windows 5 years or longer, and about half of these are never testers.

Percent of cases with a concurrent HIV/AIDS diagnosis by group.

• Consistent with the longer window lengths for non-MSM

Age distribution of never-testers by group

• Mean age at diagnosis among never-testers is 36 in MSM vs. 42 in non-MSM
  

• This will also lead to shorter windows for MSM.

Whether it's using BED, CD4, or concurrent AIDS Dx, etc

• Longer windows of possible infection for non-MSM = more uncertainty regarging time of infection, more opportunity to reallocate when these measures indicate recent infection and to improve the precision of our estimates.

• Short testing intervals in MSM = low uncertainty regarding time of infection, less potential impact of additional information

Increasing precision will not necessarily decrease undiagnosed estimates

• Modified estimates will deviate from the Base Case only to the extent that these added biomarkers indicate recent infection

• An example where this could happen is if cases with long windows tested due to risky exposure: CD4 should help pick up on that, and this would reduce the undiagnosed estimates.

Overall estimates may not change much, but our confidence in them will increase

We expect individual CD4 trajectory after HIV infection is something like this:

With CD4 steadily falling over time in the absence of treatment.

The real picture is more like this:

CD4 progressions are highly variable across individuals.

• There is still a broad trend that can be summarized
• But it is summarized in coarse categories, rather than continuous measures

The standard measure is the number of years it takes for 50% of untreated cases to reach a CD4 level threshold:

CD4 Threshold	Lodi 2011	Cori 2015	We use*
500+	1.3	2.3	1.5
350	4.3	4.2	4.0
200	7.9	8.0	8.0
< 200		11.5	9.0**

* Nearest rounded median times that are consistent with both sources. ** For CD4 < 200, we retain our maximum-window assumption of 18 years, which implies a median time of 9 years.

Interpretation: 50% of infection probability should occur within the median time.

Implication: If a case has CD4 > 500 at diagnosis, for example, we allocate 50% of the infection probability to the 1.5 years prior to Dx, and the remaining 50% to the rest of the window.

Lodi S, Phillips A, Touloumi G, Geskus R, Meyer L, Thiébaut R, et al. Time from human immunodeficiency virus seroconversion to reaching CD4+ cell count thresholds <200, <350, and <500 Cells/mm3: assessment of need following changes in treatment guidelines. Clin Infect Dis Off Publ Infect Dis Soc Am. 2011 Oct;53(8):817–25

Cori A, Pickles M, van Sighem A, Gras L, Bezemer D, Reiss P, et al. CD4+ cell dynamics in untreated HIV-1 infection: overall rates, and effects of age, viral load, sex and calendar time. AIDS Lond Engl. 2015 Nov 28;29(18):2435–46.

Example: re-allocating infection probability for an 18 year window

• Base Case: Uniform distribution, so 50% is in each half of the window (0-9] and (9-18]

Allocation of the probability of infection

Example: re-allocating infection probability for an 18 year window

• Base Case: Uniform distribution, so 50% is in each half of the window (0-9] and (9-18]

• CD4 Case: 50% of infection probability is reallocated to the CD4-based median window

Allocation of the probability of infection Base Case (red) versus CD4 Cases (blue) for the three new CD4 threshold values. Shading indicates the new placement of the initial 50% of infection probability.

Note that for cases with CD4 < 200, there is no change from the Base Case.

CD4 Category	CD4 Median	Impacts windows longer than
>500	1.5	3.0
350-500	4.0	8.0
200-350	8.0	16.0

Actual impact will depend on how much longer windows are than 2x the CD4-based median

• 18-year windows among individuals with CD4>500 will provide much greater impact than 4-year windows, for example
• Even 18-year windows will have minimal impact among CD4 200-350, since the Base Case median for 18-year windows is 9 years and the CD4-based median is 8 years (not much difference)

Why: We exclude cases when their first CD4 count is not within 30 days of HIV Dx, or if it's missing
Treatment is likely to begin soon after diagnosis, altering CD4 counts

CD4 counts among excluded cases by length of delay or missingness

• Note the longer the delay, the higher the CD4 count, which is consistent with initiation of treatment.

• It may be possible to refine this exclusion by using info on treatment initiation & viral load.

For those with a valid first CD4 measure (N=2178)

CD4 count vs infection window length, by testing status (columns) and group (rows).

• Recall that Never Testers get a window length of min(age-16, 18) years.

• Note how much variability there is, even for the short-window cases!
  ** Confirms CD4 is a very noisy (i.e., non-informative) measure of recency

CD4 distribution by testing history (colors) and group (panels).

• Shaded area indicates CD4 < 500 in never-testers.

• Suggests delayed testing, maybe in response to HIV illness-related symptoms?

• Implies the CD4 data will not modify the estimates for most of these long-window cases.

CD4 distribution by testing history (colors) and group (panels).

• Shaded area indicates CD4 > 500 in never-testers

• This is where the CD4 case has the greatest potential impact (if the never-testers are older)

Cases are modified if their observed window is at least 2x longer than the CD4-based median window

Cross-tabulation of window length by CD4 bin. Green = modified by the CD4 Case

• Percents are of the total N with testing histories(N = 3016). Dot sizes proportional to percent.

Cross-tabulation of window length by CD4 bin, by group The group with the smallest impact is CD4 = 250-300 and window > 16

• more common among non-MSM: 5%, or 5/17 = 29% of modified cases

• than MSM: 1%, or 1/7 = 14% of modified cases

Median time since infection = time by which 50% of infection probability has occurred

Estimated median time since infection under the Base Case (blue) and CD4 Case (orange) by CD4 bin.

• Among all cases with testing history (N = 3016)

• Declines are greater among the groups with higher CD4 levels.

This was a bit surprising

Why are they the same?

• Because the relative decline also depends on the starting values (Base Case estimate)*

Contributions to the relative difference in median time since infection by group.

Population	Base Case	Abs. Difference	Rel. Difference
MSM	1.94	-0.22	-11.3
non-MSM	4.50	-0.51	-11.3

Average time undiagnosed = the mean of the TID curve

Mean TID for the Base Case and CD4 Case, by MSM status

Population	Base Case	CD4 Case	Difference	Percent Change
MSM	1.83	1.72	0.11	-6.13
non-MSM	4.38	4.13	0.25	-5.74

• Again you can see the absolute decline is greater for non-MSM, but the relative decline is about the same (though slightly greater for MSM in this case)

Undiagnosed cases

Subgroups parallel the decreases in mean undiagnosed time (6.1% for MSM and 5.7% for non-MSM)

Population	Base Case	CD4 Case	Difference	Percent Change
Total	1319.0	1247.0	-72.0	-5.5
MSM	604.7	568.4	-36.3	-6.0
non-MSM	714.3	678.2	-36.1	-5.1

Undiagnosed fractions

Here the MSM declines are relatively larger: -6.5 vs. -4.0 for non-MSM

Population	Base Case	CD4 Case	Absolute Difference	Percent Change
Total	9.4	8.9	-0.5	-5.3
MSM	6.2	5.8	-0.4	-6.5
non-MSM	17.1	16.4	-0.7	-4.0

• The fractions take into account diagnosed PLWH.
  • Since the Base Case undiagnosed fraction is much higher for non-MSM, it is less sensitive than the MSM fraction to the CD4 Case's decrease of about 36 undiagnosed cases.

In WA, most cases with long windows were not recently infected

Only 10% of cases with testing history had infection windows that indicated less probability of recent infection than indicated by their CD4 count

In WA, CD4 data incorporation had the same impact on both MSM and non-MSM estimates

We expected to see greater impact in non-MSM than MSM

This was due to offsetting differences in the three components that influenced the estimate:

• Percent modified: MSM had a lower fraction of cases modified ** 7% for MSM vs 17% for non-MSM

• Size of modification: MSM had larger decreases in their median time since infection ** -2.3 yrs for MSM vs -1.9 yrs for non-MSM

• Starting values from Base Case estimates: MSM had lower base case estimates ** 6.2% for MSM vs 9.4% for non-MSM

This translated into slightly higher impacts on mean TID and mean undiagnosed estimates for MSM

We prioritize testing history data

• If testing history indicates more recent infection than CD4 does, we use the testing history
• What fraction of our LNT data is unverified self-report?
• Little is known about the accuracy of self-reports of the last negative test before diagnosis

We use CD4 conservatively

• Literature on CD4 trajectories is fairly sparse
• Data indicate plenty of heterogeneity, hence the need for using a fairly conservative approach for the CD4 Case

Our estimates now may be downwardly biased

• We are systematically including data that reduce undiagnosed estimates (e.g., CD4 or BED)
• But we are ignoring data that may increase estimates (e.g., concurrent Dx)

So we do not recommend using the CD4-based estimates for publication

Recall that we are still using the “missing at random” assumption for cases without a testing history

• But they have a higher prevalence of concurrent HIV/AIDS diagnoses
• And a lower prevalence of BED-based recent infection

• We could also use CD4 data in cases with missing testing history

  • This is one major factor that may be contributing to a downward (i.e., too optimistic) bias in our undiagnosed estimates now

Indicators of recent infection by testing history status

	Non-Missing	Missing
Percent BED +	23	8
Mean CD4	395	328
Median CD4	372	280
Percent with Concurrent Dx	30	42

• Among 3589 cases (N=70%) with CD4 measured within 30 days

Longer term: We want to integrate multiple markers

• Use a Bayesian approach to combine information from BED, CD4 and concurrent diagnoses

Among impacted cases (N = 296), density of differences in the median time since infection comparing the Base Case to the CD4 Case. Lines indicate the means of the distributions.

Mean decrease in median time since infection is slighly larger for MSM (3.10 years) than for non-MSM (3.01 years).

Among impacted cases (N = 296), density of differences in the median time since infection comparing the Base Case to the CD4 Case. Lines indicate the medians of the distributions.

Median decrease in median time since infection is slighly larger for MSM (2.34 years) than for non-MSM (1.94 years).

MSM

Time from infection to diagnosis: probability curve (top) and undiagnosed fraction curve (bottom)

non-MSM

Time from infection to diagnosis: probability curve (top) and undiagnosed fraction curve (bottom)